Chapter 6, Problem 4SGR

To determine

To find: The given statement is true or false. If false, replace underlined term to make the true sentence.

Answer to Problem 4SGR

The given statement is true.

Explanation of Solution

Given information:

The given statement: If a system has no solution, it is said to be inconsistent

Concept used:

If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent, when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.

Let a system of equations is $x+y=3$ and $-x+y=1$ , system represents two parallel lines they do not meet anywhere. So the system does not have a solution, i.e. the system of equations is inconsistent

Thus, the given statement is true.